1. Field of the Invention
The present invention relates to a measurement method and measurement device for measuring lattice strain and stress in localized regions of crystal material, and more particularly to a lattice strain measurement method and measurement device that permit an increase in measurement accuracy. The measurement method according to the present invention is particularly effective in cases of measuring lattice strain and stress of electronic devices and the like.
2. Description of the Related Art
The application of stress to crystal material of semiconductor devices and the like produces lattice strain, which in turn affects a variety of the physical properties of the crystal material. More particularly, the resultant lattice strain which accompanies the increased integration and minuteness of Ultra LSIs is one principal factor behind a variation in the element characteristics of electronic devices. Therefore, the design of a desired device necessitates measurement of the lattice strain of the electronic device crystal material, and the stress caused by this lattice strain.
Because lattice strain can be understood as being the rate of change in the lattice constant, measurement of lattice strain has conventionally involved the usage of lattice constant measurement methods such as X-ray diffraction, Raman analysis, or convergent beam electron diffraction. Of such methods, convergent beam electron diffraction is capable of determining the lattice constant with a spatial resolving power in nanometer units, and has therefore been used to measure lattice strain of minute electronic device elements. Prior art relating to such convergent beam electron diffraction includes the following methods.
Japanese Patent Applications Laid-Open Nos. 4-206941, 2000-9664, and 2001-27619 disclose methods which involve an evaluation of lattice strain in localized regions of a silicon semiconductor substrate by using a HOLZ pattern which is produced by means of extraction using convergent beam electron diffraction. Likewise, Japanese Patent Application Laid-Open No. 7-167719 and Ultramicroscopy 41(1992) Pages 211 to 223 disclose methods which involve an evaluation of lattice strain of crystal materials excluding silicon semiconductors, such as stainless steel and high temperature oxide superconductors, and the like, by using a HOLZ pattern which is produced by means of extraction using convergent beam electron diffraction.
The above methods for measuring lattice strain by using convergent beam electron diffraction are methods which measure the distances between crossing points of HOLZ (High Order Laue Zone) lines which are observed in a HOLZ pattern which is obtained by causing a convergent electron beam to impinge on crystal material, and then compare these distances with theoretical calculation values, so that the crystal material lattice strain is measured. Hence the lattice strain measurement accuracy by means of these methods is largely dependent on the accuracy of measurement of the distances between the HOLZ line crossing points.
However, the conventional measurement methods described above do not adequately consider the accuracy with which the HOLZ line crossing points are determined. For example, Japanese Patent Applications Laid-Open Nos. 4-206941 and 7-167719 make no mention of the method for determining the HOLZ line crossing points and do not direct any attention toward the determination accuracy. In addition, Japanese Patent Application Laid-Open No. 2000-9664 discloses a method that involves measuring the coordinates of several points on observed HOLZ lines, finds straight line linear equations from the measured coordinate values by means of a least square method, and determines the coordinates of crossing points by solving the straight line simultaneous equations, whereby lattice strain can ultimately be measured with an accuracy of 2.2xc3x9710xe2x88x924.
However, consideration by the present inventors revealed that with the method for determining a straight line from only a few coordinates in a formulation for specifying HOLZ lines, there was a high probability of a large error occurring. For example, in a case where a HOLZ pattern, which is obtained by causing a convergent electron beam to impinge on crystal material, is actually captured by means of image data for a pixel size of 1024xc3x971024 or more, and the ideal convergence angle of a HOLZ pattern obtained from crystal material such as silicon is 10 mrad, the lattice strain variation corresponding to one pixel is 8xc3x9710xe2x88x924. In other words, when the HOLZ-line segment extraction accuracy is one pixel, a lattice strain detection accuracy of 8xc3x9710xe2x88x924 is obtained. Therefore, in order to make lattice strain measurement feasible with an accuracy of 2.2xc3x9710xe2x88x924, there is the condition that the HOLZ-line segment extraction accuracy should be 2.2xc3x9710xe2x88x924/8xc3x9710xe2x88x924=0.275 pixel.
On the other hand, the accuracy of the least square method depends on the number of measurements, and hence, as the number of measurement points increases, the error decreases and accuracy is improved. When this fact is taken into consideration, in cases where HOLZ line is formulated from only the coordinates of a few points, it is substantially difficult to consider this error as being less than 0.3 pixel (2.2xc3x9710xe2x88x924/8xc3x9710xe2x88x924=0.275). Further, when the analysis efficiency is considered, an increase in the number of measurement coordinates to reduce the error is not considered as a suitable measure since this leads to an increase in production costs.
Accordingly, an object of the present invention is to provide a method that increases HOLZ-line segment extraction accuracy, which influences the lattice strain extraction accuracy, and that quantizes minute lattice strain in localized regions of crystal material rapidly and highly accurately.
In order to achieve the above object, one aspect of the present invention is a lattice strain measurement method that quantizes lattice strain of the crystal material in accordance with positions of HOLZ lines of a HOLZ pattern which is obtained by causing a convergent beam to impinge on crystal material constituting a measurement object, comprising the steps of: substituting coordinates of a plurality of points extracted from the HOLZ pattern for Hough transform images by means of the Hough transform, extracting clusters of a plurality of Hough transform images, and specifying HOLZ lines of the HOLZ pattern by means of reverse transformation of the clusters; and quantizing the lattice constant of the crystal material in accordance with the positions of the specified HOLZ lines.
According to the aspect of the invention described above, a plurality of points in the HOLZ pattern are substituted for a plurality of Hough transform images by means of the Hough transform, according to an image processing of image data that includes a plurality of pixels obtained by opto/electric converting a HOLZ pattern; clusters of the Hough transform images are extracted; and HOLZ lines are then specified by means of reverse transformation of these clusters. Therefore, HOLZ lines can be specified by means of predetermined calculation steps without an arbitrary HOLZ line specification step being performed by a person performing the measurement. It is thus possible to increase the accuracy with which HOLZ lines are specified.
A preferred embodiment of the above aspect of the invention is characterized by the fact that, when a plurality of points are extracted from the HOLZ pattern, points that are in the vicinity of the crossing points of the HOLZ lines are excluded from the extraction points. According to a theory known as the dynamical diffraction effect, because line disruption is generated when HOLZ lines intersect one another, crossing points are sometimes not created on account of the bending of HOLZ lines, and hence curved lines that differ from the original HOLZ lines sometimes occur in the vicinity of the HOLZ line crossing points. Therefore, the HOLZ line specification accuracy can be improved by excluding the points of such regions from the extraction points.
Further, a preferred embodiment of the aspect of the invention described above is characterized in that, when clusters of Hough transform images are extracted, points for which the cumulative value of the HOLZ pattern point concentration and the number of Hough transform images is a maximum value are extracted. Because a plurality of clusters with a large cumulative value is extracted from the above distribution of cumulative values, HOLZ lines can be specified highly accurately.